# If strings are solid, why don't they have longitudinal waves? [closed]

A string is a solid but it does not show longitudinal waves. Well it is known that a string cannot be compressed but only be given tension but a answer with a sound scientific reasoning will be accepted.

## closed as unclear what you're asking by JMac, ZeroTheHero, Jon Custer, John Rennie, M. EnnsJan 8 at 16:51

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• What is your question? – Tanner Swett Jan 8 at 5:45
• This "question" is a list of falsehoods followed by a demand. Please try to ask a question in your question. – Eric Lippert Jan 8 at 15:01

As Ben51 said, longitudinal waves do travel in strings. These don't really care how thick the material is, whether it's p-wave sound propagation through a solid block of steel or along a steel string.

There are two main reason that longitudinal modes aren't very important in string instruments:

1. They are much faster, and thus higher frequency, than the transversal modes. The p-wave velocity in iron is $$5120\:\mathrm{\tfrac{m}s}$$ (unlike for the transversal modes, this doesn't change much with tension/thickness), so a $$650\:\mathrm{mm}$$ guitar string will have a longitudinal fundamental mode at $$7880\:\mathrm{Hz}$$. Ok, that's still audible to most humans, but it's far away from the range of fundamentals where you'd actually play notes fundamental mode at $$3940\:\mathrm{Hz}$$, much higher than the 80-300 Hz range where the strings have their musical pitches. So at most this will contribute some extra percussion to the timbre, not actual tone that's heard as such.
2. There's no effective way to excite them. The string may be physically able to vibrate longitudinally, but how do you get it to do so? Plucking, hitting, bowing all excite mostly the transversal modes. To excite a longitudinal mode, you'd need to somehow pull along the string in either direction and release the extra tension, but to pull you'd need to really grab it and then it's very hard to release quickly enough to not immediately damp the vibration again. So even a longitudinal mode that's well in the audible range will usually barely sound during playing.

I do think longitudinal modes happen and are audible in some cases; I suspect they contribute to the somewhat bell-like sound of very low tones on a grand piano. In actual tubular bells, they are probably quite loud, even. But they are hardly musically useful.

The $$7880\:\mathrm{Hz}$$ figure was a thought mistake. The wave actually travels twice the length of the string in each cycle (from the bridge to the nut and back).

• As an aside: the modes that are acoustically important in tubular bells are flexural. That is, they're due to bending, with the material's own stiffness (rather than external tension) as the restoring force. – Michael Seifert Jan 7 at 22:29
• @MichaelSeifert right. The transversal modes of thick strings also have such a contribution in their restoring force, though that's generally considered an undesirable side-effect, causing inharmonicity by detuning the harmonics upwards. – leftaroundabout Jan 7 at 22:35
• @leftaroundabout I think point 2 suggest a third reason: it's hard to interact with longitudinal waves in both directions. What I mean is, once you've excited the string longitudinally, how does it transmit back out to the air? The transverse waves of the string move the air around as they pass through it, longitudinal waves only move air through friction. – Cramer Jan 7 at 23:36
• @Cramer no, that's not much of a point. The transversal modes also transmit only very little energy to air; most of what you hear from a guitar string comes from the body's resonance of the string vibration. And such resonance could use the longitudinal component just as well as a transversal one, just attach the string at a steep angle to a sound board. J Thomas gave the harp as an example. – leftaroundabout Jan 7 at 23:52
• ...your point might be interesting underwater though: here, the direct emission of sound waves from the strings is much stronger, in fact so strong that it pretty much damps the strings immediately. Thus, the longitudinal modes might actually become more relevant in this case, because they are less damped. – leftaroundabout Jan 7 at 23:54

Longitudinal waves do propagate in string. That is how "tin can phones" work.

• So in other words you have to pre-tension the string so it never tries to go into compression. – immibis Jan 8 at 5:35

Why would you expect it not to have longitudinal waves?

If you have a steel bar and you hammer on one end, you get compression waves. They travel as fast as the inter-atomic forces transmit them from one atom to another.

If a string is under tension, and you hammer backward against whatever it's tied to, I'd expect the string to transmit tension waves. The amount of tension would increase and decrease, and the waves would travel as fast as the inter-atomic forces transmit them from one atom to another.

It makes perfect sense that when you pluck a string under tension, you make both transverse and longitudinal waves. Beginning physics students pay attention to the longitudinal waves because they are a metaphor for transverse light waves, and they can be visible.

So when you make a guitar or a violin, does the sound come from the transverse waves from the string causing the air inside the sound box to vibrate, which causes the front panel to vibrate, which vibrates the air outside the soundbox?

Or is is from the longitudinal waves from the string causing the neck and bridge of the instrument to vibrate, which causes the front panel to vibrate, which vibrates the air inside and outside the soundbox.

If it's the latter, you could make a stringed instrument that had the soundbox at one end with the strings attached to it normal to the surface, and it would make sound even though the strings' transverse motion doesn't have much opportunity to affect the soundbox or the air inside it.

And you can.

So is it more likely that this instrument has its sounding board vibrated by the longitudinal tension of the strings, or the air moved by their transverse motion?

• The “played tone” mode for harp strings is clearly transversal like in guitars. Whether longitudinal modes are audible too I'm not sure, but they're definitely no more than a secondary contribution to the sound. – leftaroundabout Jan 7 at 21:43
• You think? How could it be tested? How could it be tested for a guitar? Here's a thought. Get a second guitar with no strings. Put it close to a working guitar. If you pluck the strings and the guitar which is not touching the strings makes loud notes, then it's definitely not longitudinal tension waves doing it. Can you think of a test that could show it isn't transverse waves in the air that are doing it, if in fact it isn't that? – J Thomas Jan 8 at 2:38
• That test would not provide any conclusions as to transversal vs longitudinal: the second guitar would stay quiet either way. Both transversal and longitudinal components would only be audible through the rigid mechanical connection to the sound box, i.e. through the bridge. But, for why the longitudinal mode isn't important, see my answer. – leftaroundabout Jan 8 at 10:28
• You and I agree that what's important is what happens at the end of the string (or anyway at the bridge). The string actually moving sideways contributes little sound, the string making the wood vibrate is the important part. I'm unclear how that happens. I imagine it might be a pressure change. The string pushes against the bridge, and the wave motion results in it pushing more or less, and that makes the wood vibrate. – J Thomas Jan 8 at 16:29
• It's the transverse motion of the string that makes it happen. You stretch the string sideways. The string stores the energy, inertia keeps it stretching side to side, its' the mass of the string.... Or is it that the string is a spring which contracts and releases, alternately tugging on its attachments and letting go? It's both. – J Thomas Jan 8 at 16:34